[Chapter 12] Linear Optimization Models

Highland Marketing Group is a full-service marketing research company. Highland is being hired to interview registered voters in a district to gain insights into their opinions about certain issues. Each voter is to be interviewed in person. The cost of interviewing different types of voters varies due to the differences in the population. Based on previous studies, estimates of the interviewing costs for different types of voters are given in the table below.

	Cost Per Interview
	Democrat	Republican	Independent
City	$18	$16	$22
Suburbs	$21	$20	$25

The contract called for Highland to conduct interviews under the requirements (as detailed in the Constraints section) given below. Please help Highland develop an interview plan by formulating a linear optimization model.

I. Define the decision variables.

(Note: This step is done for you. Please use these decision variables hereafter.)

X₁ = Number of voters who are Democrats and from the City interviewed;

X₂ = Number of voters who are Republicans and from the City interviewed;

X₃ = Number of voters who are Independents and from the City interviewed;

X₄ = Number of voters who are Democrats and from the Suburbs interviewed;

X₅ = Number of voters who are Republicans and from the Suburbs interviewed;

X₆ = Number of voters who are Independents and from the Suburbs interviewed.

Question 4 (2 points)

At most 40% of the total voters interviewed may be Republicans.

Question 4 options:

	X2 + X5 > 0.4 (X1 + X2 + X3 + X4 + X5 + X6)
	X2 + X5 0.4 (X1 + X2 + X3 + X4 + X5 + X6)
	X2 + X5 0.4 (X1 + X2 + X3 + X4 + X5 + X6)
	X2 + X5 0.4 X1 + X2 + X3 + X4 + X5 + X6
	X2 + X5 0.4 X1 + X2 + X3 + X4 + X5 + X6
	X2 + X5 < 0.4 (X1 + X2 + X3 + X4 + X5 + X6)
	X2 + X5 0.4
	X2 + X5 0.4